What are the divisors of 4136?

1, 2, 4, 8, 11, 22, 44, 47, 88, 94, 188, 376, 517, 1034, 2068, 4136

There is a total of 16 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 540.

12 even divisors

2, 4, 8, 22, 44, 88, 94, 188, 376, 1034, 2068, 4136

4 odd divisors

1, 11, 47, 517

How to compute the divisors of 4136?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 4136 by each of the numbers from 1 to 4136 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

4136 / 1 = 4136 (the remainder is 0, so 1 is a divisor of 4136)
4136 / 2 = 2068 (the remainder is 0, so 2 is a divisor of 4136)
4136 / 3 = 1378.6666666667 (the remainder is 2, so 3 is not a divisor of 4136)
...
4136 / 4135 = 1.0002418379686 (the remainder is 1, so 4135 is not a divisor of 4136)
4136 / 4136 = 1 (the remainder is 0, so 4136 is a divisor of 4136)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 4136 (i.e. 64.311740763254). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

4136 / 1 = 4136 (the remainder is 0, so 1 and 4136 are divisors of 4136)
4136 / 2 = 2068 (the remainder is 0, so 2 and 2068 are divisors of 4136)
4136 / 3 = 1378.6666666667 (the remainder is 2, so 3 is not a divisor of 4136)
...
4136 / 63 = 65.650793650794 (the remainder is 41, so 63 is not a divisor of 4136)
4136 / 64 = 64.625 (the remainder is 40, so 64 is not a divisor of 4136)